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Biostatistics Advance Access published online on October 14, 2009
Biostatistics, doi:10.1093/biostatistics/kxp041
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Bayesian random-effects threshold regression with application to survival data with nonproportional hazards

Michael L. Pennell*

Division of Biostatistics, College of Public Health, The Ohio State University, 320 West 10th Avenue, Columbus, OH 43210, USA, mpennell{at}cph.osu.edu

G. A. Whitmore

Department of Mathematics and Statistics, Desautels Faculty of Management, McGill University, Montreal, Canada

Mei-Ling Ting Lee

Department of Epidemiology and Biostatistics, School of Public Health, University of Maryland, College Park, MD, USA

* To whom correspondence should be addressed.

In epidemiological and clinical studies, time-to-event data often violate the assumptions of Cox regression due to the presence of time-dependent covariate effects and unmeasured risk factors. An alternative approach, which does not require proportional hazards, is to use a first hitting time model which treats a subject's health status as a latent stochastic process that fails when it reaches a threshold value. Although more flexible than Cox regression, existing methods do not account for unmeasured covariates in both the initial state and the rate of the process. To address this issue, we propose a Bayesian methodology that models an individual's health status as a Wiener process with subject-specific initial state and drift. Posterior inference proceeds via a Markov chain Monte Carlo methodology with data augmentation steps to sample the final health status of censored observations. We apply our method to data from melanoma patients with nonproportional hazards and find interesting differences from a similar model without random effects. In a simulation study, we show that failure to account for unmeasured covariates can lead to inaccurate estimates of survival probabilities.

Keywords: Bayesian methodology; Nonproportional hazards; Random effects; Survival analysis; Threshold regression; Wiener process

Received September 23, 2008; revised September 11, 2009; accepted for publication September 14, 2009.


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